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Derive three-dimensional exponential (3DX) weights

Source: R/weights_threedx.R
weights_threedx.Rd

Assigns weights that decay in three different directions as determined by the combination of weights_exponential(), weights_seasonal(), and weights_seasonal_decay().

Usage

weights_threedx(alpha, alpha_seasonal, alpha_seasonal_decay, n, period_length)

Arguments

alpha

The smoothing factor passed to weights_exponential() that determines the overall monotonic exponential weight component

alpha_seasonal

The smoothing factor passed to weights_seasonal() that determines the exponential weighting within a seasonal period

alpha_seasonal_decay

The smoothing factor passed to weights_seasonal_decay() that determines the exponential weighting of the seasonal periods

n

The number of weights to create; this is usually equal to the number of observations in a time series

period_length

The length of the seasonal period to be modeled

Value

A numeric vector of n values between 0 and 1 that sum up to 1

See also

weights_exponential(), weights_seasonal(), weights_seasonal_decay()

Examples

weights <- weights_threedx(
  alpha = 0.01,
  alpha_seasonal = 0.05,
  alpha_seasonal_decay = 0.01,
  n = 17,
  period_length = 5
)

print(weights)
#>  [1] 0.05115383 0.05439003 0.05841513 0.05605492 0.05379007 0.05433341
#>  [7] 0.05777077 0.06204605 0.05953914 0.05713352 0.05771063 0.06136164
#> [13] 0.06590267 0.06323993 0.06068478 0.06129776 0.06517572

if (require("ggplot2")) {
  ggplot2::ggplot(
    data.frame(index = seq_along(weights), weight = weights),
    ggplot2::aes(x = index, y = weight)
  ) +
    ggplot2::geom_col()
}


# random walk forecast
weights_threedx(
  alpha = 1,
  alpha_seasonal = 0,
  alpha_seasonal_decay = 1,
  n = 30,
  period_length = 12
)
#>  [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

# mean forecast
weights_threedx(
  alpha = 0,
  alpha_seasonal = 0,
  alpha_seasonal_decay = 0,
  n = 30,
  period_length = 12
)
#>  [1] 0.03333333 0.03333333 0.03333333 0.03333333 0.03333333 0.03333333
#>  [7] 0.03333333 0.03333333 0.03333333 0.03333333 0.03333333 0.03333333
#> [13] 0.03333333 0.03333333 0.03333333 0.03333333 0.03333333 0.03333333
#> [19] 0.03333333 0.03333333 0.03333333 0.03333333 0.03333333 0.03333333
#> [25] 0.03333333 0.03333333 0.03333333 0.03333333 0.03333333 0.03333333

# seasonal mean forecast
weights_threedx(
  alpha = 0,
  alpha_seasonal = 1,
  alpha_seasonal_decay = 0,
  n = 30,
  period_length = 12
)
#>  [1] 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5
#> [20] 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

# seasonal naive forecast
weights_threedx(
  alpha = 0,
  alpha_seasonal = 1,
  alpha_seasonal_decay = 1,
  n = 30,
  period_length = 12
)
#>  [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

# last year's mean forecast
weights_threedx(
  alpha = 0,
  alpha_seasonal = 0,
  alpha_seasonal_decay = 1,
  n = 30,
  period_length = 12
)
#>  [1] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#>  [7] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [13] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [19] 0.08333333 0.08333333 0.08333333 0.08333333 0.08333333 0.08333333
#> [25] 0.08333333 0.08333333 0.08333333 0.08333333 0.08333333 0.08333333